High-pressure fuel pumps, in particular piston pumps for a fuel system for an internal combustion engine, are available in the market. Such high-pressure fuel pumps often include an inlet valve and a discharge valve which may open and close as a function of a control and/or as a function of a fuel pressure. The discharge valve allows a fuel accumulator (“rail”) that is under pressure to close against a delivery space of the high-pressure fuel pump during a suction stroke. In contrast, if a fuel pressure in the delivery space exceeds a counterforce resulting from the pressure in the fuel accumulator, plus a closing spring force, the discharge valve may open.